Feynman rules for Gauss's law

TL;DR

This paper develops Feynman rules incorporating Gauss's law constraint in gauge theories, analyzing the effects of a Lagrange multiplier field on confinement and phase structure.

Contribution

It introduces a method to include Gauss's law via a Lagrange multiplier in perturbation theory, revealing its impact on non-Abelian gauge theory phases.

Findings

Effective potential for the Lagrange multiplier influences confinement.

Different solutions for the multiplier lead to various phases.

Radiative effects generate a potential affecting gauge interactions.

Abstract

I work on a set of Feynman rules that were derived in order to incorporate the constraint of Gauss's law in the perturbation expansion of gauge field theories and calculate the interaction energy of two static sources. The constraint is implemented via a Lagrange multiplier field, $\lambda$, which, in the case of the non-Abelian theory, develops a radiatively generated effective potential term. After analysing the contributions of various solutions for $\lambda$, the confining properties and the various phases of the theory are discussed.